Echelon Form of Matrix
Echelon Form of Matrix:
An m n matrix A is said to be in reduced row echelon form if it satiesfy the following properties:
1. All zero rows, if there are any appear at the bottom of the matrix.
2. The first entry from the left of a non-zero row is 1. This entry is called a leading one of its row.
3. For each non zero row, the leading one appear to the right and below any leading one in precedding rows.
4. If a column contain a leading one then all other entry in that column are zero.
A matrix is reduced row echelon from appears as a staircase pattern of leading 1s descedending from the upper left corner of the matrix. An m n matrix satiesfies all above the properties.
Example-1: The following are matrices in reduced row echelon form:
Interchange row 1 and row 3;
Multiplying the 3rd of A by 1/3 we get;